Madurai Kamraj University (MKU) 2007 B.Sc Mathematics TENA - Question Paper

TENA

6255/M3A    OCTOBER 2007

Paper X THEORY OF EQUATIONS AND NUMERICAL ANALYSIS

(For those who joined in July 2003 and after)

Time : Three hours    Maximum : 100 marks

SECTION A (8 x 5 = 40 marks)

Answer any EIGHT questions.

1.    If one root of the equation 2x³ - llx² + 38x - 39 = 0 is 2-3i, find the other roots.

2.    Solve x⁴ + 4x³ - 2a:² - 12x +9 = 0, given that it has two pairs of equal roots.

3.    Transform the equation x³ + px² +qx + r = Ointo another, locking the second degree term.

4.    Show that the equation x^s + qx + r = Owill have one root twice another if 343 r² + 36q³ = 0 .

5.    Show that x³ + 3x - 1 = 0 has only one real root and calculate it correct to two places of decimals.

7.    Find a real root of the equation cosx = 3x - 1 correct to 4 decimal places by iteration method.

8.    Solve the following system of equations, using Gauss-Jordan method

x - y + ^z - 1, ^_ 3x + 2y - 3z = - 6, 2x - 5y + 4z = 5.

6255/M3A    OCTOBER 2007

X

e^x -- =e^x, taking h as the

6255/M3A    OCTOBER 2007

K:e^x

interval of differencing.

10.    By dividing the range into ten equal parts,

n

evaluate J sinxofo: by Trapezoidal rule. Verify your

o

answer with actual integration.

11.    Find the missing term in the following :

*: 1 2 3 4 5 6 7 y: 2 4 8 - 32 64 128

12.    Solve u_n - 2u_n + u_n _ ₂ = 0.

SECTION B (6 x 10 = 60 marks)

Answer any SIX questions.

13.    Solve the equation actanac - -1 by Regula Falsi method starting with a = 2.5 and 6 = 3 correct to 3 decimal places.    i

14.    Solve, by Gauss-Seidel method the following system

28x + 4y - 2 = 32, x + 3y + 10z = 24, 2x + 17y + 4z = 35.

15.    Using the following table, apply Gauss forward formula to get f (3.75)

x: 2.5 3.0 3.5 4.0 4.5 5.0

f(x): 24.145 22.043 20.225 18.644 17.262 16.047

16.    Use Stirlings formula to get tan8926' from the table

x: 8921' 8923' 8925' 8927' 8929 tanx : 88.14 92.91 98.22 104.17 110.90

17.    Find a cubic polynomial ofx given that

x: 0 12 5 fix): 2 3 12 147

18.    Find the age corresponding to the annuity value 13.6 given the table :

Age (x):    30 35 40 45 50

Annuity value (y): 15.9 14.9 14.1 13.3 12.5

19.    Find the values of _{y z}A?x² and _{y z} A² x³ and hence evaluate , A² (ax + 6) ((x +d) and

j* *

_{y z} A² (ax + b) ((x +d) ilx + f).

20.    Evaluate I = J log_e x dx using (a) Simpsons

4

and (b) Weddles rule.

21.    Solve y_n+2 - 4y_n+1 + 3y_n = 2" + 3" + 7.

22.    Solve Au_x + A²u_x = cosx .

Attachment: madurai-kamraj-university--mku--2007-b-sc-mathematics-21873-1.pdf

Earning:   Approval pending.